# AbstainGNN: Teaching Graph Neural Networks to Abstain for Graph Classification

arXiv: https://arxiv.org/abs/2605.30786 · HTML: https://mlsanity.com/paper/2605.30786/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 25 of its 50 references that are in the map.
- First posted on arXiv 29 May 2026.

## Builds on (most cited first, 25 of 25)

- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learning](https://mlsanity.com/paper/1506.02142/) (2015)
- [How Powerful are Graph Neural Networks?](https://mlsanity.com/paper/1810.00826/) (2018)
- [Neural Message Passing for Quantum Chemistry](https://mlsanity.com/paper/1704.01212/) (2017)
- [A Comprehensive Survey on Graph Neural Networks](https://mlsanity.com/paper/1901.00596/) (2019)
- [MoleculeNet: A Benchmark for Molecular Machine Learning](https://mlsanity.com/paper/1703.00564/) (2017)
- [Selective Classification for Deep Neural Networks](https://mlsanity.com/paper/1705.08500/) (2017)
- [TUDataset: A collection of benchmark datasets for learning with graphs](https://mlsanity.com/paper/2007.08663/) (2020)
- [SelectiveNet: A Deep Neural Network with an Integrated Reject Option](https://mlsanity.com/paper/1901.09192/) (2019)
- [A PAC-Bayesian Approach to Spectrally-Normalized Margin Bounds for Neural Networks](https://mlsanity.com/paper/1707.09564/) (2017)
- [A Fair Comparison of Graph Neural Networks for Graph Classification](https://mlsanity.com/paper/1912.09893/) (2019)
- [Weisfeiler and Lehman Go Topological: Message Passing Simplicial Networks](https://mlsanity.com/paper/2103.03212/) (2021)
- [A Survey on Graph Kernels](https://mlsanity.com/paper/1903.11835/) (2019)
- [Graph Learning: A Survey](https://mlsanity.com/paper/2105.00696/) (2021)
- [Self-Adaptive Training: beyond Empirical Risk Minimization](https://mlsanity.com/paper/2002.10319/) (2020)
- [Trustworthy Graph Neural Networks: Aspects, Methods and Trends](https://mlsanity.com/paper/2205.07424/) (2022)
- [Rethinking pooling in graph neural networks](https://mlsanity.com/paper/2010.11418/) (2020)
- [Deep Gamblers: Learning to Abstain with Portfolio Theory](https://mlsanity.com/paper/1907.00208/) (2019)
- [Classification with Rejection Based on Cost-sensitive Classification](https://mlsanity.com/paper/2010.11748/) (2020)
- [On the Calibration of Multiclass Classification with Rejection](https://mlsanity.com/paper/1901.10655/) (2019)
- [Efficient Active Learning with Abstention](https://mlsanity.com/paper/2204.00043/) (2022)
- [An end-to-end attention-based approach for learning on graphs](https://mlsanity.com/paper/2402.10793/) (2024)
- [Boosting Graph Pooling with Persistent Homology](https://mlsanity.com/paper/2402.16346/) (2024)
- [Confidence-aware Contrastive Learning for Selective Classification](https://mlsanity.com/paper/2406.04745/) (2024)

## Abstract (arXiv)

Graph classification is a core task in graph data mining with widespread real-world applications. Recent advances in graph neural networks (GNNs) have led to substantial performance improvements for graph classification. However, existing GNNs are typically forced to make predictions even under high uncertainty or unknown conditions, resulting in unreliable decisions that can severely impact downstream tasks, particularly in safety-critical scenarios. To address this critical limitation, we propose AbstainGNN, a novel and theory-driven framework for graph classification with abstention, which enables GNNs to reject uncertain predictions instead of producing incorrect decisions. Specifically, AbstainGNN explicitly models both the predictive function and the abstention function, allowing for effective utilization of graph structural information. Moreover, unlike existing heuristic abstention methods, we theoretically characterize the trade-off between classification errors and rejection costs from a PAC-Bayesian generalization perspective, and derive a unified learning objective for model optimization. Guided by this theoretical insight, we further develop an efficient two-stage training strategy consisting of predictive function warm-start and abstention function calibration. Extensive experiments on five benchmark datasets show that AbstainGNN outperforms existing abstention methods, achieving superior classification performance under the same rejection rates.